Linear relationships

A linear relationship is one where one quantity changes by the same amount every step, like a phone plan that costs the same each month or a tank that drains at a steady rate. Its graph is a straight line. In Year 7 you solved simple equations and plotted points from a rule. In this topic you'll solve harder equations, draw and read straight-line graphs on the Cartesian plane, find where two lines meet, and work with inequalities, which describe a whole range of answers instead of just one.

What you'll learn

• 6.01 Solve equations: one- and two-step equations with negatives, fractions and brackets, and checking a solution by substitution.
• 6.02 Tables of values: completing tables from a rule, finding the rule from a table, and using tables to model real situations.
• 6.03 Linear graphs: plotting straight lines, reading the intercepts and the gradient, horizontal and vertical lines, and reading answers from graphs.
• Investigation: linear solutions. Use graphing software to see why every point on a line is a solution of its equation, and to solve equations with graphs.
• 6.04 Multi-step equations: equations with the pronumeral on both sides, brackets and fractions.
• 6.05 Intersecting lines: finding where two lines meet, from a graph and with algebra, and what that point means in real problems.
• 6.06 Inequalities: the symbols <, >, ≤ and ≥, showing inequalities on a number line, and solving them.
• Investigation: experiment with linear inequalities. Find out what keeps an inequality true, and use graphing software to shade regions on the number plane.

Which level should I pick?

Every worksheet comes in three levels. Each one covers the same skills.

• Level 1 · Warm-up: smaller numbers and more help along the way. A good place to start.
• Level 2 · Core: the main worksheet for the lesson.
• Level 3 · Challenge: fractions, negatives and problems with more steps, for when the Core level feels easy.

Not sure? Start with Level 2. If the first few questions feel tricky, drop to Level 1. If you finish quickly and get them right, try Level 3. Download the worksheet, print it, and write your answers in the boxes.

Practice tests

When you've finished the lessons, try the three practice tests. Each one is like the real topic test: 45 minutes, 40 marks, a section without a calculator and a section with one. Write your working under each question, then copy your final answers onto the answer sheet on the last page, just like you will in the real test.